Problem: Let $A = (3, \theta_1)$ and $B = (9, \theta_2)$ in polar coordinates.  If $\theta_1 - \theta_2 = \frac{\pi}{2},$ then find the distance $AB.$
Explanation: Let $O$ be the origin.  Then $\angle AOB = \frac{\pi}{2},$ so by Pythagoras,
\[AB = \sqrt{3^2 + 9^2} = \boxed{3 \sqrt{10}}.\][asy]
unitsize(0.5 cm);

pair A, B, O;

A = 3*dir(100);
B = 9*dir(10);
O = (0,0);

draw(A--O--B--cycle);

draw((-2,0)--(10,0));
draw((0,-1)--(0,4));

label("$A$", A, NW);
label("$B$", B, E);
label("$O$", O, SW);
[/asy]